Amp is the SI unit of measurement for current.
Volt is the SI unit of measurement for voltage.

When you apply a voltage across a material, a current will flow within it.
The resistance of the material will determine how much current flows:
simply: [tex] V = I R [/tex]

Voltage is a 'measure' of potential between two locations with different electrical charge distributions. Current is the rate of flow of electrical charge with respect to time.

A simple analogy to compare is considering a water flow in a pipe, only replace the water with electrical charge or electrons.

The voltage is the water pressure.
The current is the rate of water flow.
The resistance is the size of the pipe's cross-section.

So for narrow pipes (high resistance - poor conductor) you need a high pressure (voltage) to drive the water (current) through.

But for big pipes (low resistance - good conductor) you only need a small pressure (voltage) to drive the water (current) through.

So for a given material with a 'constant' resistance, you will need to increase your voltage in order to increase your current. But you can change your material to a lesser resistance material, so that it is easier to drive a current through.
Hope that helps.

In a simple metal there is one electron loosley bound to each atom , and relatively free to move , not quite free. They keep on bumping into the atoms sometimes recombine . This lack of freedom in motion we call resistance.
When the electrons experience a force causing them to move in one direction -- they move in a 'random walk' or drift with an average speed . This motion we call 'current'.
The AMP is a measure of how many electrons move past a given point when drifting due to a force.

Generally the 'force' is caused or comes about because we have separated electrons from where they wish to be , which is as close as possible to a proton which carries the opposite and attractive charge , located in the atomic nucleus.

In a metal the total number of protons equals the number of electrons -- so the whole is electrically neutral . however it takes 'work ' to separate them ( because there is a force of attraction .
Voltage is defined as the amount of work required to separate charges ( on some unit basis ). It exists because those charges wish to get back together.
If allowed to do so then there is a flow of electrons back from whence they came ( a current) , and experiences some difficulties doing so ( resistance).

SOOOOoo V=I.R tells you that the amount of work is proportional to the rate of electon flow x the difficulty in getting there.
V is one of the hardest electrical units to understand , but in physics it is clinically defined as Joules per coulomb -- the amount of mechanical work done per unit charge in moving charges away from an opposite charge or towards a repelling charge .
We can easilly see current flow , and we can easilly see resistance , but V we cannot see , unless you visualise it as the toil required to do something ( in Human terms that is ).

Just for fun... in everyday household appliances the 'net' movement of electrons through a wire is just millimeters per second! quite a paradox seeing as we are used to electrons travelling very quickly...